I have an edge that does not bevel as expected, what might be wrong?
Beveling ngons (faces with more than 4 vertices) is not a good idea : results are not really predictable.

Here is a view of the inner geometry with triangles (on the right) :



The upper part of your mesh is good, but the ngon part does not allow to manipulate it well (for beveling, for instance).

So for a good bevel, you should redo this part with quads only (faces composed of 4 vertices), the same way you modeled the upper part.

Also take care of the bottom part (on the left) which is composed of 5 vertices. 

To 'repair' the mesh


Go to edit mode
First of all, select all and remove double vertices (some are doubled)
Set face selection mode by Ctrl + Tab then face
Select the two faces which are ngons then delete this faces (X then 'only faces')





Set vertices selection mode by Ctrl + tab then 'vertex'
Select the vertices like below in order to count them (here 18)





Give 18 cut on the bottom part (Ctrl+R then Page Up 17 times)





Select the top and bottom vertices on one side (without the extremities)
Then Ctrl+E and 'bridge edge loops'





Do the same for the other side


Now we have this below, so simply complete the faces for the extremities.




Beveling :